We present static electric dipole polarizabilities alpha(d)(Z, N) from numerical nonrelativistic restricted Hartree-Fock (RHF) finite-field calculations for high-spin open-shell S states (L - 0) of atoms and isoelectronic ions with N <= 55 electrons. All these S states result from one or more half-filled shells. For eight isoelectronic sequences, those with N = 3, 7, 11, 15, 23, 29, 33 or 41 electrons where the electronic ground state of the neutral or nearly neutral members is conserved upon increase of the nuclear charge number Z, polarizability data are given for ions with charge number Q = Z - N up to Q = 90. In addition, these data are represented in terms of rational functions of Q (with absolute value of the relative error of the fit always below 4%). The rational functions are comparable to the classical nonrelativistic result alpha(d)(Z, 1) = 4.5/Z(4) = 4.5/(Q + 1)(4) for the polarizability of the S-2 ground state of a hydrogen-like system. Our results also contribute to constitute a reference database (i) for algebraic approaches relying on basis functions, and (ii) for the discussion of relativistic and correlation effects on polarizabilities along isoelectronic sequences.